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Hydrodynamic

Mechanisms in PlantTissues during MassTransportOperations

P. Fito, A. Chiralt, J. Martnez-Monz, and J. Barat

CONTENTS

8.1 Introduction

8.2 HDM Promoted by External Pressure Changes

8.3 HDM Promoted by Cell Shrinkage in Osmotic Processes

8.4 HDM Promoted by Cell Matrix Relaxation in Long-Term

Osmotic Processes8.5 Conclusions

Nomenclature

Acknowledgments

References

8.1 INTRODUCTION

In the processing of fruit and vegetables, solidfluid systems (SFS) frequently occurin different operations, such as osmotic dehydration, rehydration, candy processing,

boiling, and cooking, among others. The heat and mass transfer processes in such

systems have usually been modeled considering the food solid as a continuous phase.

Nevertheless, the cellular structure (intercellular spaces and cell compartmentation)

plays an important role in the definition of mechanisms involved in the process and

therefore in process kinetics. Recently, several studies have been carried out to

determine the influence of porosity on the response of fruit tissue to solidliquid

operations (Fito, 1994; Fito and Pastor, 1994; Fito et al., 1996; Fito and Chiralt,

1997). In this way, a fast mass transfer mechanism (hydrodynamic mechanism,HDM) has been described as occurring in process operations in which a porous solid

is immersed in a liquid phase; changes in temperature or pressure also take place.

The occluded gas inside the product pores is compressed or expanded according

to the pressure or temperature changes, while the external liquid is pumped into the

8

2003 by CRC Press LLC

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pores in line with the gas compression. An effective exchange of the product internal

gas with the external liquid is promoted in vacuum impregnation (VI) operations,

where a vacuum pressure (p1~50100 mbar) is imposed on the system for a short

time (t1); afterwards, the atmospheric pressure (p2) is reestablished while the product

remains immersed in the liquid for a time t2 (Fito et al., 1996; Salvatori et al., 1998a).

The volume fraction of the initial sample (X) impregnated by the external liquid

when mechanical equilibrium is achieved in the sample has been modeled as a function

of the compression ratio r (given by Equation (8.1), where pc is capillary pressure),

sample effective porosity (e), and sample volume deformations at the end of theprocess () and the vacuum step (1) (Equation (8.2)) (Fito et al., 1996). If = 1 = 0,Equation (8.1) gives the relationship for VI of stiff products.

(8.1)

(8.2)

When there are no pressure changes (p1 = p2) in the system, capillary impreg-nation will occur due to the capillary pressure; the lower the pressure in the system,

the greater the liquid penetration, according to Equations (8.1) and (8.2).

The possibility of introducing an external solution containing specific/selected

solutes inside the product pores has made VI a tool in fruit processing. The addition of

preservatives (antimicrobials, antibrowning agents, pH reducers, and others) or nutrients(minerals, vitamins, etc.), fast water activity depression, and modifying physical prop-

erties, among others, may be some of the possible applications of VI (Chiralt et al., 1999).

Impregnation of the fruit pores due to hydrodynamic mechanisms has been seen

to occur without external pressure changes when the cellular tissue remains

immersed in a liquid phase for a long time (e.g., syrup canned and candied fruits).

This has been explained in terms of the capillary forces, pressure and temperature

fluctuations in the system, and relaxation phenomena of the shrunken cellular matrix

when hypertonic solutions are used in the treatments (Barat et al., 1998). Fito et al.

(2000) reported a contribution of HDM to the total mass transfer throughout theosmotic process due to the pressure gradients in the tissue associated with internal

volume generation in line with cell water losses.

The aim of this work is to analyze the role of hydrodynamic mechanisms in

different kinds or times of processing in plant tissuefluid systems and their impli-

cations in process kinetics, as well as the influence of the action of these mechanisms

on plant tissues in terms of product quality or process advantages.

8.2 HDM PROMOTED BY EXTERNAL PRESSURE CHANGESThe most effective action of HDM in the product pores is promoted by vacuum

impregnation operations. The compression ratio can reach very high values by using

common industrial pumps and, additionally, the product remains are impregnated at

the end of the process when normal pressure is recovered. Impregnation promoted by

rp p

p

c=+

2

1

e

r X r( ) ( ) = +11


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applying high pressure in the system is not effective because the liquid introduced into

the pores in the compression step flows out when the system returns to atmospheric

conditions. For stiff matrices, the kinetics of impregnation are very fast, depending on

the pore size (length and diameter) and tortuosity and the liquid viscosity. Equation

(8.3) gives the relationship between the liquid penetration level and time, in terms of

the volume fraction of the pore impregnated (xv) at time t (t2) in a reduced way (xr)

(Equation (8.4)).The value of xve corresponds to the impregnated volume at mechanical

equilibrium, which can be obtained by Equation (8.2) when = 1 = 0, since xv = X/e.Parameters B and k are described by Equations (8.5) and (8.6) (Chiralt et al., 1999).

(8.3)

(8.4)

(8.5)

(8.6)

Figure 8.1 shows the predicted development of xr as a function of time (t2) after

the vacuum step for different values of the external liquid viscosity, and by consid-

ering a stiff matrix with pore size of 100 m diameter, 1 cm length, and a tortuosityfactor Ft = 2. It can be observed that even for high viscosity liquids such ashydrocolloids or concentrated sugars, the penetration times needed to reach the xveare on the order of a few minutes (Figure 8.1a). This process length is near the time

required to achieve stationary pressure in the tank after the valve is opened to restore

the atmospheric pressure.

In real systems with a viscoelastic character, the kinetics of pore impregnation

are coupled with deformationrelaxation of the sample volume. A fast mechanical

pseudoequilibrium can be achieved in the first step, with a notable reduction of

product porosity coupled with partial liquid penetration. Afterwards, the true equi-

librium is reached through relaxation of the deformed porous matrix, which leads

to progressive liquid entry in line with sample volume recovery while the product

remains immersed. This two-step behavior will be especially promoted when long

penetration times, associated with high liquid viscosity or/and small pore diameter,

occur. For cylindrical (2 cm diameter and height) apple samples, Figure 8.1b shows

the sample volume fraction impregnated (X) and deformed () after VI (10 min at50 mbar) with a sugar isotonic solution and with 3% pectin sugar isotonic solution,

as a function of the length of the VI second step at atmospheric pressure. It can be

observed that at very short times, the sample volume reduces by about 5% and

slowly recovers in line with time increase. The impregnation levels increase more

quickly in the less viscous solution.

t

Bx x k x x

x

xr r r rr

r

= +

1

2

1

1

2

0

2

0

0

( ) ( ) ln

x xxr

v

ve

=

kx

ve

= +11

BeF

r

p

p pt

p

=

8

2

2

2 1

2

( )


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It is remarkable that when solutions with high viscosity are used for VI, it is

advantageous to carry out the vacuum step with samples suspended above the

solution, rather than immersed in it. If not, difficulties of sample gas outflow cause

great sample deformation and very limited impregnation. Throughout the release of

the gas, it becomes entrapped in the external solution, thus forming stable foam

around the sample with much higher viscosity than the original fluid. During the

second VI step, part of the entrapped gas flows into the pores again, thus reducing

the impregnation effectiveness.

Table 8.1 shows the levels of deformation and impregnation of cylindrical apple

samples at the end of the vacuum step and of the process as a function of the

FIGURE 8.1 (a) Impregnation kinetics of an ideal pore (100 m diameter, 1 cm length, 2tortuosity factor) for different viscosities (Pa s) of the external solution. (b) Development of

sample volume fraction impregnated (X, closed symbols) and deformed (, open symbols)with time (t2), during VI of cylindrical apple (var. Granny Smith) samples with isotonic sugar

solution (squares) and 3% pectin isotonic sugar solution (circles).

(a)

0

0.2

0.4

0.6

0.8

1

0 20 40 60

t (s)

xr

(m3/m

3)

0.01 Pas

0.1 Pas

1.0 Pas

(b)

-0.1

0

0.1

0.2

0 1000 2000 3000 4000t(s)

X/


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impregnating solution viscosity. Effective sample porosity, calculated by Equation

(8.2), assuming mechanical equilibrium, also appears in Table 8.1. The decreasing

values of e, in line with the solution viscosity increase, suggest that mechanicalequilibrium was not reached for t2 = 15 min. On the other hand, a greater effectivenessof sample impregnation when the sample is not immersed in the viscous solution

during the vacuum step can be observed.

VI may promote fast compositional changes in fruit, which is useful in many cases

to ensure processed fruit stability (decrease of pH or water activity, introduction of

antibrowning agents or microbial preservatives) or quality (the improvement of the

sweetsour taste relationship, fortification with specific nutrients). Prediction of com-

positional changes in short VI treatments can be easily obtained by applying Equations

(8.7) and (8.8), if the value of the impregnated volume fraction (X) and the densityof the initial product (0) and the impregnating solution (IS) are known (Chiralt et al.,1999). From these equations, the required solution mass fraction (yi) of a determined

component (i.e., water, sugar, acid, additive, etc.) to achieve the desired level in the

final product (mass fraction: xiVI

) can be calculated. Composition changes promoted

by concentration gradients between external solution and product were not taken into

account in Equation (8.7) due to the short length of VI processes. In Equation (8.7),

xi0

corresponds to the initial mass fraction of component i in the product.

(8.7)

(8.8)

TABLE 8.1Impregnation (X) and Deformation () Levels of Apple (var. GrannySmith) Cylindrical Samples (2 cm Diameter and Height) Reached in a

VI Operation (p1 = 50 mbar, t1 = 10 min, t2 = 15 min) with IsotonicSugar Solutions Containing Different Concentrations of Pectin

Pectinconcentration

%Viscosity (Pas) X1

a 1a

Xb b e

c

0 0.0068 0.035 0.013 0.14 0.05 0.201 0.0202 0.043 0.03 0.12 0.02 0.152 0.0917 0.011 0.10 0.07 0.05 0.143 0.179 0.028 0.14 0.09 0.06 0.133d 0.179 0.040 0.01 0,13 .0,05 0.19

aAt the end of the vacuum step.

bAt the end of the process.

cDetermined on the basis of theoretical model (Equation (8.2)) assuming mechanical equilibrium.

dSamples were not immersed in the solution during the vacuum step.

x x x y

xiVI i HDM i

HDM

= ++

0

1

x XHDM

IS

=0


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8.3 HDM PROMOTED BY CELL SHRINKAGEIN OSMOTIC PROCESSES

Throughout osmotic processes in fruit and vegetables, a great cell volume reduction

occurs due to intracellular water loss. This implies the generation of internal voids

that provoke internal pressure depression, which promotes hydrodynamic flow ofthe external solution from the sample interface to the internal voids. These pressure

gradients also contribute to the structural development pathway of cells, depending

on the kind of fluid (gas or liquid) in the tissue pores (Fito et al., 2000).

Figure 8.2 shows a scheme of how HDMs were promoted into the tissue, as well

as the sample cellular structure development. When the intercellular spaces are full of

liquid, osmosis promotes plasmolysis but no significant folding of the cell wall,

whereas the space between plasmalemma and cell wall is flooded by the extracellular

liquid (Martnez-Monz et al., 1998a). In contrast, when intercellular spaces are occu-

pied by gas, osmosis provokes cell wall shrinkage without plasmalemma separations

(Salvatori et al., 1998b). This difference in behavior has been explained in terms of

the different pressure drop of gas or liquid phases during their flux towards the

intercellular space generated volumes (isgv in Figure 8.2). The balance of forces acting

on both sides of the plasmalemmacell wall layer during cell water volume loss leads

to the separation of the double layer and to the flux of the external liquid through the

cell wall, or to cell wall deformation together with the plasmalemma (Fito et al., 2000).

In osmotic treatments of cellular tissues, HDM may act to a great extent at the

beginning of the process if a vacuum pulse is applied in the tank for a short period

(Pulsed Vacuum Osmotic Dehydration, PVOD), since the sample impregnation with

the osmotic solution is promoted. In treatments at atmospheric conditions (OD) or

at vacuum conditions (Vacuum Osmotic Dehydration, VOD) capillary pressure also

provokes HDM near the sample interface to a lesser extent. The different extent of

the external liquid flow into the tissue and the subsequent differences in the cellular

structure development will affect the tissue response to mass transport.

Figure 8.3 shows a comparison of the effective diffusivity values (De) in the fruit

liquid phase obtained in OD and PVOD treatments in apple slices (1 cm thick)

FIGURE 8.2 Scheme of cellular structure development during osmotic treatments dependingon the fluid present in the intercellular spaces (is) and water (Jw) and hydrodynamic (JHDM)

fluxes (isgv, intercellular space generated volume; ic, intracellular content; A and B, cell

bonding points).

Jw

is

A

B

JHDM

is containing liquid phase

is containing gas phase

A

B

is

JWJHDMM

ic

isgv


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osmosed with different sucrose syrups (2565Brix) at 30, 40, and 50C. Compo-sitional change promoted by the vacuum pulse was corrected to make the De values

more comparable (Barat et al., 1997). Higher values of De in the PVOD process can

be observed; the higher the De value in OD, the greater the difference.

On the other hand, Figure 8.4 shows the influence of VI with isotonic solutions

of different viscosity on the kinetics of fruit liquid phase composition changes for

apple cylindrical samples. The reduced concentration of each component (Yi) was

defined in terms of the solute or water mass fractions (zi, i = water or solutes) inthe fruit liquid phase (water plus solutes) by Equation (8.9). The value of z at equi-

librium (zie) was taken to be equal to that of the osmotic solution. The acceleration

of kinetics in line with the filling of the pores, without any changes in the initial

value of the process driving force, can be observed. Nevertheless, if the impregnating

FIGURE 8.3 Comparison of values of the effective diffusion coefficient (De, in m2

/sec) inapple (Granny Smith) liquid phase (water plus solutes) obtained in OD and PVOD processes

carried out with different sucrose solutions (25 to 65Brix) at 30, 40, and 50C.

FIGURE 8.4 Kinetics of fruit liquid phase composition changes in cylindrical apple samples(2 cm diameter and height) osmosed in 62Brix rectified grape must, for nonimpregnated

samples (), samples impregnated with an isotonic solution (), and samples impregnatedwith a 3% pectin isotonic solution ( ).

0

2

4

6

8

10

12

0 2 864 10 12

De 1010

(m2/s)(OD)

De

1

010(m2/s)(PVOD)

25 Brix

35 Brix

45 Brix55 Brix

65 Brix

-0.8

-0.7

-0.6

-0.5

-0.4-0.3

-0.2

-0.1

0

0 4000 8000 12000t (s)

Ln Y


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solution viscosity is high, slower kinetics are observed. These results agree with a

great promotion of diffusion through the noncompartmented intercellular spaces

when filled with liquid phase, which is greatly affected by the liquid viscosity

(Martnez-Monz et al., 1998b).

(8.9)

8.4 HDM PROMOTED BY CELL MATRIX RELAXATIONIN LONG-TERM OSMOTIC PROCESSES

In long-term osmotic processes such as those carried out in fruit candying, HDM

plays an important role in tissue development after compositional equilibrium

between the sample and the external solution has been reached. Sample mass and

volume decrease in line with osmotic dehydration until a minimum value is reached

at compositional equilibrium time tc. From this point, sample mass and volume begin

a slowly increasing pathway until almost all of the initial values are recovered. This

was observed initially in apple samples (Barat et al., 1998; Fito et al., 1998) and

was confirmed for other fruits (Barat, 1998).

Mass and sample volume recovery has been explained in terms of pressure

gradients generated in the shrunken cellular structure due to relaxation of cell walls,

where a great amount of free energy was stored during cell dehydrationshrinkage.

True equilibrium in the system implies free energy reduction by release of mechan-

ical stress. If the product remains immersed in the external solution, volume recovery

is coupled with liquid suction and therefore with mass gain. In this sense, the pressure

drop of liquid inflow will affect the sample volume relaxation rate, causing the

system (fruit plus external liquid) to behave as a viscoelastic solid. The overall

relaxation rate of the system will be greatly dependent on liquid viscosity and the

elastic character of the cellular matrix. The relative relaxation level will be deter-

mined by the total volume lost during osmotic treatment and the irreversible struc-

tural damage in the tissue. In this sense, cellular turgor will not be recovered, and

so the final sample volume will be reduced with respect to the initial value by the

intercellular volume associated with the turgid cell packaging.

HDM flow in this matrix relaxation process has been modeled on the basis of

a viscoelastic model (Equation (8.10)) (Peleg, 1980). In Equation (8.10), F0 and Ft are

respectively the initial force on the sample associated with a given deformation and

the force at a determined relaxation time. The constants A and B represent, respec-

tively, the total relative relaxation level and the relaxation rate. To fit Equation (8.10)

to the experimental mass recovery data, the following hypotheses are considered:

the mechanical stress on the matrix is released as flow pressure drops in the external

liquid; likewise, a laminar flow was assumed. From these hypotheses, force will be

given by Equation (8.11), thus obtaining Equation (8.12) to describe mass recovery.

The M0

values are the relative mass gain of the sample at each time. The function

(dM0(t)/dt) was obtained by fitting a bi-exponential function to the experimental

Yz z

z zii

t

i

e

i i

e=

( )

( )0


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curve (M0

vs. time) and calculating the derivative equation and its values at each

time.

(8.10)

(8.11)

(8.12)

Figure 8.5 shows a linear relationship between experimental points plotted as

defined by Equation (8.12) for OD and PVOD treatments of 1 cm thick apple slices,

with 55Brix sucrose solution, at 30, 40, and 50C. The scarce influence of temper-ature and kind of treatment on the kinetics of HDM mass flow during sample stress

relaxation can be observed. Table 8.2 shows the mean values obtained for A and B

parameters for OD and PVOD treatments of apple slices in the 3050C range. Thevalues of A are near one in all cases, indicating that samples recover about 100%

of their initial mass throughout the examined time, with the relaxation rate being

affected by the syrup concentration. The relaxation is faster as the sucrose concen-tration is lower (below 25Brix), in agreement with the lower viscosity values ofthe solutions.

FIGURE 8.5 Kinetics of HDM mass flow in long-term osmotic processes after compositionalequilibrium time (tc). Points correspond to osmosed apple slices (1 cm thick) in 55Brixsucrose solution for OD and PVOD treatments at different temperatures.

F t

F F AB

t

At

0

0

1

= +

FF e M t

tt

IS=

( )

8 0

( ( ) / )

( ( ) / ) ( ( ) / )

= = +M t t t

M t t M t t

t

Y AB

t

At F

0

00

0

0

1

0

1000

2000

3000

4000

0 1000 2000 3000 4000

t tc (h)

t/YF (h)

55 OD 30C55 OD 40C55 OD 50C55 PVOD 30C

55 PVOD 40C55 PVOD 50C


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8.5 CONCLUSIONS

HDM plays an important role in solidliquid operations with cellular products such

as fruit and vegetables. Through understanding and modeling the action of these

mechanisms, better process control will be possible. Promotion of these mechanisms

through the control of process variables may be a tool in designing new product

composition.

NOMENCLATURE

p Pressure (mbar), (subscript c: capillary; 1: at the vacuum step; 2: atmospheric)

Solution viscosity (Parsec)xv Pore volume fraction impregnated by the solution (m

3/m

3)

xve Pore volume fraction impregnated by the solution at mechanical equilibrium

(m3/m

3)

xr Reduced pore volume fraction impregnated by the solution (xv/xve)

e Sample effective porosityr Compression ratio

X1 Sample volume fraction impregnated by the solution at the end of the first

VI step

X Sample volume fraction impregnated by the solution at the end of the VI

process

1 Relative volume deformation of the sample due to pressure change at theend of the first VI step

Relative volume deformation of the sample due to pressure change at theend of the VI process

e Sample characteristic dimension (m)

rp Pore radius (m)

Ft Tortuosity factor of the sample pores

TABLE 8.2A and B Parameters of Equation (10) for OD and PVOD

Treatments of Osmosed Apple Slices in Sucrose Syrups

(OS) of Different ConcentrationsOD PVOD

Brix (OS) A B A B

65 1.02 0.002 0.98 0.009

55 1.05 0.004 1.07 0.005

45 1.02 0.012 1.05 0.037

35 1.01 0.024 1.00 0.094

25 0.98 0.162 0.96 0.082

20 1.01 0.024 1.01 0.080


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k Dimensionless parameter of the model of VI kinetics

B Time dimension parameter of the model of VI kinetics

0 Density of the initial product (kg/m3)IS Density of the impregnating solution (kg/m3)xHDM Mass ratio of the impregnated solution in the initial product (kg/kg)

yiiv Mass fraction of the component i in the impregnating solution (kg/kg)

xi0 Mass fraction of component i in the impregnated product (kg/kg)

xi Mass fraction of component i in the initial product (kg/kg)

Yi Reduced driven force referred to component i

zt

i Mass fraction of component i in the food liquid phase at time t of the process

(kg/kg)

De Pseudodiffusion coefficient (m2/sec)

M0

Mass relative change of the sample at each time (kg/kg)

t Process time (sec)

F Force (N)

ACKNOWLEDGMENTS

The authors thank the Comisin Interministerial de Ciencia y Tecnologa (Spain),

CYTED program, and European Union (DGXII) for their financial support.

REFERENCES

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